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165
Tabela G.4: Comparação do erro da variável de interesse ( I
DDS−2
) entre as quatro formas de
aplicar as condições de contorno
x
DDS−2
∆
I
I
DDS−2
x
DDS−2
∆
I
x
DDS−2
∆
Sem vol fict Com vol fict
Com meio vol
Com esp zero
0,33333 0,41927 0,41927 0,5 1,11164 0,33333 0,41927
0,11111 0,02847 0,02847 0,25 0,10127 0,11111 0,02847
0,03704 0,00439 0,00439 0,125 0,02226 0,03704 0,00439
0,01235 9,50234E-4 9,50234E-4 0,0625 0,00522 0,01235 9,50234E-4
0,00412 2,60625E-4 2,60625E-4 0,03125 0,00127 0,00412 2,60625E-4
0,00137 8,0654E-5 8,0654E-5 0,01562 3,12581E-4 0,00137 8,0654E-5
4,57247E-4 2,61938E-5 2,61938E-5 0,00781 7,76207E-5 4,57247E-4 2,61938E-5
1,52416E-4 8,65451E-6 8,65451E-6 0,00391 1,93408E-5 1,52416E-4 8,65451E-6
5,08053E-5 2,87631E-6 2,87631E-6 0,00195 4,82724E-6 5,08053E-5 2,87631E-6
1,69351E-5 9,57822E-7 9,57822E-7 9,76563E-4 1,20582E-6 1,69351E-5 9,57822E-7
5,64503E-6 3,19169E-7 3,19169E-7 4,88281E-4 3,01331E-7 5,64503E-6 3,19169E-7
1,88168E-6 1,06378E-7 1,06378E-7 2,44141E-4 7,53172E-8 1,88168E-6 1,06378E-7
6,27225E-7 3,5458E-8 3,5458E-8 1,2207E-4 1,88274E-8 6,27225E-7 3,5458E-8
2,09075E-7 1,18192E-8 1,18192E-8 6,10352E-5 4,7066E-9 2,09075E-7 1,18192E-8
6,96917E-8 3,93971E-9 3,93971E-9 3,05176E-5 1,17662E-9 6,96917E-8 3,93971E-9
2,32306E-8 1,31324E-9 1,31324E-9 1,52588E-5 2,94151E-10 2,32306E-8 1,31324E-9
7,62939E-6
3,8147E-6
1,90735E-6
9,53674E-7
4,76837E-7
2,38419E-7
1,19209E-7
5,96046E-8
2,98023E-8
1,49012E-8
7,35374E-11
1,83843E-11
4,59606E-12
1,14902E-12
2,87254E-13
7,18134E-14
1,79534E-14
4,48834E-15
1,12208E-15
2,80521E-16
I
A Tab. G.5 mostra as ordens obtidas com a forma de aplicar as condições de contorno
com volume fictício, mas o mesmo resultado é verificado com as formas sem volume fictício
e com volume de espessura zero e a Tab. G.6 mostra os resultados das ordens obtidas com a
forma de aplicar as condições de contorno com meio-volume.
Tabela G.5: Ordens assintótica, efetiva e aparente do erro de discretização para a variável de
u com a forma com volume fictício
∆ x
interesse ( )
nod
pE
pL nod
nod
pU
nod
Fonte numérico
Fonte numérico
0,333333333333333 2,00000000000000
0,111111111111111 2,00000000000000 2,45317465262878
0,0370370370370370 2,00000000000000 2,04780930823578 2,49093332598021
0,0123456790123457 2,00000000000000 2,00512106464860 2,05297458650728
0,00411522633744856 2,00000000000000 2,00056702029548 2,00568832395652
0,00137174211248285 2,00000000000000 2,00006297837903 2,00063000101228
4,57247370827618E-4 2,00000000000000 2,00000699730382 2,00006997571085
1,52415790275873E-4 2,00000000000000 2,00000077747458 2,00000777477874
5,08052634252909E-5 2,00000000000000 2,00000008638602 2,00000086386060
1,69350878084303E-5 2,00000000000000 2,00000000959845 2,00000009598447
5,64502926947676E-6 2,00000000000000 2,00000000106649 2,00000001066494
1,88167642315892E-6 2,00000000000000 2,00000000011850 2,00000000118499
6,27225474386307E-7 2,00000000000000 2,00000000001316 2,00000000013167
2,09075158128769E-7 2,00000000000000 2,00000000000137 2,00000000001463
6,96917193762563E-8 2,00000000000000 2,00000000000079 2,00000000000144
2,32305731254188E-8 2,00000000000000 2,00000000138341 1,99999999982796